Question 31327: Solve the equation
log(3+x) - log(3-x) = log3
Thanks for your help!!!! Found 2 solutions by Fermat, stanbon:Answer by Fermat(136) (Show Source):
You can put this solution on YOUR website! One of the rules of logarithms is,
logA - logB = log(A/B)
Applying this rule to your eqn,
log{(3+x)/(3-x)} = log(3)
Since you have the log of something on one side of the equation equals the log of something else on the other side then we can say that the something on the one side equals the something else on the other side, giving,
(3+x)/(3-x) = 3
multiply both sides by (x-3), to give
3 + x = 3(3-x) = 9 - 3x
4x = 6
x = 1.5
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You can put this solution on YOUR website! Rule: logA - logB= log (A/B)
Your problem rewritten is:
log[(3+x)/(3-x)]= log 3
Take the anti-log to get:
(3+x)/(3-x)=3
3+x=3(3-x)
3+x=9-3x
4x=6
x=(3/2)
Cheers,
Stan H.
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